Different types of neologisms have different functions, which is most vivid in literary texts, and may prove a true a challenge for their translator. The present paper examines the issue in the context of the Polish translations of A Clockwork Orange by Anthony Burgess. Interestingly enough, the novel was translated into Polish by (the late) Robert Rouven Stiller twice and exists in two versions: the Russianized Mechaniczna pomarańcza (1989/1999; A Mechanical Orange: referred to by Stiller as version R) and the Americanized Nakręcana pomarańcza (1999; A Wind-Up Orange: named version A by the translator). Applying the relevance-theoretic tools in the analysis of the corpus of neologisms from the source text and its translations, it is demonstrated how the cognitive effects created by the alternative translations vary, and the consequences that follow for the target reader are discussed. The results afford insights about the nature of neologisms on the one hand, and on the other, lead to useful implications about translation theory and practice. In fact, this kind of approach, as will be postulated, can be productively used in raising awareness of would-be translators: by exploring the different kinds of effects that different renderings yield, translation students become more conscious of how their translation choices may affect the target audience’s reception of the text.